A higher-order generalization of an A₄ ⁽¹⁾ -surface type q-Painlevé equation with W((A2N⋊A₁)⁽¹⁾×A₁ ⁽¹⁾) symmetry

Recently, a birational representation of an extended affine Weyl group of A 2 N ⋊ A 1 1 -type, which gives a higher-order generalization of an A 4 1 -surface type q -Painlevé equation, was obtained. In this paper, we extend it to a birational representation of an extended affine Weyl group of A 2 N ⋊ A 1 1 × A 1 1 -type. Moreover, we provide conjectures on periodic reductions from systems of PΔEs with the CAC property to Painlevé type q -OΔEs.